Empirical solutions via the adaptive learning network methodology have been obtained to measure characteristics of three-dimensional defects (spherical and spheroidal) from the analysis of theoretically-modeled scattered waveforms. The solutions have been successfully applied to measure defects from actually observed ultrasonic scattering data. Spherical voids and inclusions in Ti-6-4, varying in diameter from 0.02 em to 0.12 em, and varying In acoustic impedance ratio !with respect to the host alloy (Ti-6-4)] from zero for air cavities to four for tungsten-carbide inclusions, can be directly measured via: (i) The phase cepstrum - which yields an unambiguous measurement of defect diameter and is independent of its acoustic impedance ratio; (ii) Adaptive Learning Networks (ALN) - synthesized from the amplitude spectrum and which yield accurate measurements of defect diameter and the acoustic impedance ratio of the included material. The two empirical solutions. synthesized from the scattering data from an exact model for spheres, yield similar accurate results when applied to actual scattering observed from the defects. Spheroidal defects (oblate spheroids) varying in aspect ratio from 1.67 to 6, varying in volume from 20 to 310 millionths of a cubic centimeter, and varying in orientation from 0°· to 360° in azimuth and 0° to 90° in elevation, can be measured by adaptive learning networks synthesized from scattering data produced by the Born approximation as the theoretical model. Scattering data used to train the ALNs were obtained via computer simulation. As in the case of spheres, the ALNs were trained-using the synthetic waveforms--to predict the defect size and orientation. Once the empirical models were obtained, eight actual defect sizes and orientations were found via the models and these results compare well with the true values. This paper will describe the means by which the inversion of ultrasonic scattering to defect characteristics was accomplished and its NDE implications.